(* Content-type: application/vnd.wolfram.mathematica *)

(*** Wolfram Notebook File ***)
(* http://www.wolfram.com/nb *)

(* CreatedBy='Mathematica 11.3' *)

(*CacheID: 234*)
(* Internal cache information:
NotebookFileLineBreakTest
NotebookFileLineBreakTest
NotebookDataPosition[       158,          7]
NotebookDataLength[     50970,       1199]
NotebookOptionsPosition[     49022,       1164]
NotebookOutlinePosition[     49408,       1181]
CellTagsIndexPosition[     49365,       1178]
WindowFrame->Normal*)

(* Beginning of Notebook Content *)
Notebook[{

Cell[CellGroupData[{
Cell[BoxData[{
 RowBox[{
  RowBox[{"Remove", "[", "\"\<Global`*\>\"", "]"}], 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"Clear", "[", "\"\<`*\>\"", "]"}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"a11", "=", 
   RowBox[{
    RowBox[{"-", "r"}], "*", 
    RowBox[{"Sin", "[", "\[Lambda]", "]"}], 
    RowBox[{"Cos", "[", "\[Theta]", "]"}]}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"a12", "=", 
   RowBox[{
    RowBox[{"-", "r"}], "*", 
    RowBox[{"Cos", "[", "\[Lambda]", "]"}], 
    RowBox[{"Sin", "[", "\[Theta]", "]"}]}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"a13", "=", 
   RowBox[{
    RowBox[{"Cos", "[", "\[Lambda]", "]"}], 
    RowBox[{"Cos", "[", "\[Theta]", "]"}]}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"a21", "=", 
   RowBox[{"r", "*", 
    RowBox[{"Cos", "[", "\[Lambda]", "]"}], 
    RowBox[{"Cos", "[", "\[Theta]", "]"}]}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"a22", "=", 
   RowBox[{
    RowBox[{"-", "r"}], "*", 
    RowBox[{"Sin", "[", "\[Lambda]", "]"}], 
    RowBox[{"Sin", "[", "\[Theta]", "]"}]}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"a23", "=", 
   RowBox[{
    RowBox[{"Sin", "[", "\[Lambda]", "]"}], 
    RowBox[{"Cos", "[", "\[Theta]", "]"}]}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"a31", "=", "0"}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"a32", "=", 
   RowBox[{"r", "*", 
    RowBox[{"Cos", "[", "\[Theta]", "]"}]}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"a33", "=", 
   RowBox[{"Sin", "[", "\[Theta]", "]"}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"A", "=", 
   TagBox[
    RowBox[{"(", "\[NoBreak]", GridBox[{
       {"a11", "a12", "a13"},
       {"a21", "a22", "a23"},
       {"a31", "a32", "a33"}
      },
      GridBoxAlignment->{
       "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
        "Rows" -> {{Baseline}}, "RowsIndexed" -> {}},
      GridBoxSpacings->{"Columns" -> {
          Offset[0.27999999999999997`], {
           Offset[0.7]}, 
          Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
          Offset[0.2], {
           Offset[0.4]}, 
          Offset[0.2]}, "RowsIndexed" -> {}}], "\[NoBreak]", ")"}],
    Function[BoxForm`e$, 
     MatrixForm[BoxForm`e$]]]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"iA", "=", 
   RowBox[{"Simplify", "[", 
    RowBox[{"Inverse", "[", "A", "]"}], "]"}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"G", "=", 
   RowBox[{"Simplify", "[", 
    RowBox[{
     RowBox[{"Transpose", "[", "A", "]"}], ".", "A"}], "]"}]}], 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"iG", "=", 
   RowBox[{"Simplify", "[", 
    RowBox[{"Inverse", "[", "G", "]"}], "]"}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"sqrtG", "=", 
   RowBox[{"Simplify", "[", 
    RowBox[{
     RowBox[{"Sqrt", "[", 
      RowBox[{"Det", "[", "G", "]"}], "]"}], ",", 
     RowBox[{"r", ">", "0"}]}], "]"}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"dGdlon", "=", 
   RowBox[{"MatrixForm", "[", 
    RowBox[{"Simplify", "[", 
     RowBox[{"D", "[", 
      RowBox[{"G", ",", "\[Lambda]"}], "]"}], "]"}], "]"}]}], 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"dGdlat", "=", 
   RowBox[{"MatrixForm", "[", 
    RowBox[{"Simplify", "[", 
     RowBox[{"D", "[", 
      RowBox[{"G", ",", "\[Theta]"}], "]"}], "]"}], "]"}]}], 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"dGdr", "=", 
   RowBox[{"MatrixForm", "[", 
    RowBox[{"Simplify", "[", 
     RowBox[{"D", "[", 
      RowBox[{"G", ",", "r"}], "]"}], "]"}], "]"}]}], 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{"Print", "[", 
  RowBox[{"\"\<A=\>\"", ",", 
   RowBox[{"MatrixForm", "[", "A", "]"}]}], "]"}], "\[IndentingNewLine]", 
 RowBox[{"Print", "[", 
  RowBox[{"\"\<iA=\>\"", ",", 
   RowBox[{"MatrixForm", "[", "iA", "]"}]}], "]"}], "\[IndentingNewLine]", 
 RowBox[{"Print", "[", 
  RowBox[{"\"\<G=\>\"", ",", 
   RowBox[{"MatrixForm", "[", "G", "]"}]}], "]"}], "\[IndentingNewLine]", 
 RowBox[{"Print", "[", 
  RowBox[{"\"\<iG=\>\"", ",", 
   RowBox[{"MatrixForm", "[", "iG", "]"}]}], "]"}], "\[IndentingNewLine]", 
 RowBox[{"Print", "[", 
  RowBox[{"\"\<sqrtG=\>\"", ",", "sqrtG"}], "]"}], "\[IndentingNewLine]", 
 RowBox[{"Print", "[", 
  RowBox[{"\"\<dGdlon=\>\"", ",", "dGdlon"}], "]"}], "\[IndentingNewLine]", 
 RowBox[{"Print", "[", 
  RowBox[{"\"\<dGdlat=\>\"", ",", "dGdlat"}], "]"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"Print", "[", 
   RowBox[{"\"\<dGdr=\>\"", ",", "dGdr"}], "]"}], "\[IndentingNewLine]", 
  "\[IndentingNewLine]", 
  RowBox[{"(*", 
   RowBox[{
    RowBox[{"https", ":"}], "//", 
    RowBox[{
     RowBox[{
      RowBox[{"zhuanlan", ".", "zhihu", ".", "com"}], "/", "p"}], "/", 
     "37451449"}]}], "*)"}]}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"v", "=", 
   RowBox[{"{", 
    RowBox[{"\[Lambda]", ",", "\[Theta]", ",", "r"}], "}"}]}], 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"dg1", "=", 
   RowBox[{"Outer", "[", 
    RowBox[{"D", ",", "G", ",", "v"}], "]"}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{"dg2", "=", 
    RowBox[{"Transpose", "[", 
     RowBox[{"dg1", ",", 
      RowBox[{"{", 
       RowBox[{"1", ",", "3", ",", "2"}], "}"}]}], "]"}]}], ";"}], 
  RowBox[{"(*", 
   RowBox[{"change", " ", "indices", " ", "orders"}], 
   "*)"}]}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"dg3", "=", 
   RowBox[{"Transpose", "[", 
    RowBox[{"dg1", ",", 
     RowBox[{"{", 
      RowBox[{"2", ",", "3", ",", "1"}], "}"}]}], "]"}]}], ";"}], "\n", 
 RowBox[{
  RowBox[{
   RowBox[{"CS", "=", 
    RowBox[{"Simplify", "[", 
     RowBox[{
      RowBox[{"(", 
       RowBox[{"1", "/", "2"}], ")"}], 
      RowBox[{"iG", ".", 
       RowBox[{"(", 
        RowBox[{"dg1", "+", "dg2", "-", "dg3"}], ")"}]}]}], "]"}]}], ";"}], 
  RowBox[{"(*", 
   RowBox[{"christoffel", " ", "symbols"}], "*)"}]}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"Print", "[", 
   RowBox[{"\"\<Christoffel=\>\"", ",", 
    RowBox[{"MatrixForm", "[", "CS", "]"}]}], "]"}], "\[IndentingNewLine]", 
  "\[IndentingNewLine]"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"OmegaCart", "=", 
   RowBox[{"\[Omega]", "*", 
    RowBox[{"{", 
     RowBox[{"0", ",", "0", ",", "1"}], "}"}]}]}], 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{"OmegaSphContra", "=", 
    RowBox[{"FullSimplify", "[", 
     RowBox[{"iA", ".", "OmegaCart"}], "]"}]}], ";"}], 
  RowBox[{"(*", 
   RowBox[{"Omega", " ", "in", " ", "Contravariant", " ", "sense"}], "*)"}], 
  "\[IndentingNewLine]", 
  RowBox[{"(*", 
   RowBox[{"Omega", " ", "in", " ", "Physical", " ", "sense"}], 
   "*)"}]}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"OmegaSph", "=", "OmegaSphContra"}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"OmegaSph", "[", 
   RowBox[{"[", "1", "]"}], "]"}], "=", 
  RowBox[{"Simplify", "[", 
   RowBox[{
    RowBox[{
     RowBox[{"OmegaSphContra", "[", 
      RowBox[{"[", "1", "]"}], "]"}], "/", 
     RowBox[{"Sqrt", "[", 
      RowBox[{"iG", "[", 
       RowBox[{"[", 
        RowBox[{"1", ",", "1"}], "]"}], "]"}], "]"}]}], ",", 
    RowBox[{"r", ">", "0"}]}], "]"}]}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"OmegaSph", "[", 
   RowBox[{"[", "2", "]"}], "]"}], "=", 
  RowBox[{"Simplify", "[", 
   RowBox[{
    RowBox[{
     RowBox[{"OmegaSphContra", "[", 
      RowBox[{"[", "2", "]"}], "]"}], "/", 
     RowBox[{"Sqrt", "[", 
      RowBox[{"iG", "[", 
       RowBox[{"[", 
        RowBox[{"2", ",", "2"}], "]"}], "]"}], "]"}]}], ",", 
    RowBox[{"r", ">", "0"}]}], "]"}]}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{"OmegaSph", "[", 
    RowBox[{"[", "3", "]"}], "]"}], "=", 
   RowBox[{"Simplify", "[", 
    RowBox[{
     RowBox[{
      RowBox[{"OmegaSphContra", "[", 
       RowBox[{"[", "3", "]"}], "]"}], "/", 
      RowBox[{"Sqrt", "[", 
       RowBox[{"iG", "[", 
        RowBox[{"[", 
         RowBox[{"3", ",", "3"}], "]"}], "]"}], "]"}]}], ",", 
     RowBox[{"r", ">", "0"}]}], "]"}]}], "\[IndentingNewLine]", 
  "\[IndentingNewLine]", 
  RowBox[{"(*", 
   RowBox[{
   "Centrifugal", " ", "Force", " ", "in", " ", "Physical", " ", "sense"}], 
   "*)"}]}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"CentrifugalForceCart", "=", 
   RowBox[{
    SuperscriptBox["\[Omega]", "2"], 
    RowBox[{"{", 
     RowBox[{
      RowBox[{"Cos", "[", "\[Lambda]", "]"}], ",", 
      RowBox[{"Sin", "[", "\[Lambda]", "]"}], ",", "0"}], "}"}]}]}], 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"CentrifugalForceSph", "=", 
   RowBox[{"iA", ".", "CentrifugalForceCart"}]}], 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"CentrifugalForceSph", "[", 
   RowBox[{"[", "1", "]"}], "]"}], "=", 
  RowBox[{"Simplify", "[", 
   RowBox[{
    RowBox[{
     RowBox[{"CentrifugalForceSph", "[", 
      RowBox[{"[", "1", "]"}], "]"}], "/", 
     RowBox[{"Sqrt", "[", 
      RowBox[{"iG", "[", 
       RowBox[{"[", 
        RowBox[{"1", ",", "1"}], "]"}], "]"}], "]"}]}], ",", 
    RowBox[{"r", ">", "0"}]}], "]"}]}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"CentrifugalForceSph", "[", 
   RowBox[{"[", "2", "]"}], "]"}], "=", 
  RowBox[{"Simplify", "[", 
   RowBox[{
    RowBox[{
     RowBox[{"CentrifugalForceSph", "[", 
      RowBox[{"[", "2", "]"}], "]"}], "/", 
     RowBox[{"Sqrt", "[", 
      RowBox[{"iG", "[", 
       RowBox[{"[", 
        RowBox[{"2", ",", "2"}], "]"}], "]"}], "]"}]}], ",", 
    RowBox[{"r", ">", "0"}]}], "]"}]}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{"CentrifugalForceSph", "[", 
    RowBox[{"[", "3", "]"}], "]"}], "=", 
   RowBox[{"Simplify", "[", 
    RowBox[{
     RowBox[{
      RowBox[{"CentrifugalForceSph", "[", 
       RowBox[{"[", "3", "]"}], "]"}], "/", 
      RowBox[{"Sqrt", "[", 
       RowBox[{"iG", "[", 
        RowBox[{"[", 
         RowBox[{"3", ",", "3"}], "]"}], "]"}], "]"}]}], ",", 
     RowBox[{"r", ">", "0"}]}], "]"}]}], 
  "\[IndentingNewLine]"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"GravityCart", "=", 
   RowBox[{"-", 
    RowBox[{"{", 
     RowBox[{
      RowBox[{"r", "*", 
       RowBox[{"Cos", "[", "\[Lambda]", "]"}], 
       RowBox[{"Cos", "[", "\[Theta]", "]"}]}], ",", 
      RowBox[{"r", "*", 
       RowBox[{"Sin", "[", "\[Lambda]", "]"}], 
       RowBox[{"Cos", "[", "\[Theta]", "]"}]}], ",", 
      RowBox[{"r", "*", 
       RowBox[{"Sin", "[", "\[Theta]", "]"}]}]}], "}"}]}]}], 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{"GravitySph", "=", 
  RowBox[{"g", "*", 
   RowBox[{"Normalize", "[", 
    RowBox[{"Simplify", "[", 
     RowBox[{"iA", ".", "GravityCart"}], "]"}], 
    "]"}]}]}], "\[IndentingNewLine]"}], "Input",
 CellChangeTimes->{{3.748150017387987*^9, 3.7481501002669964`*^9}, {
   3.7481502531342697`*^9, 3.748150351134679*^9}, {3.7481503817956753`*^9, 
   3.748150396240039*^9}, 3.7481504415937014`*^9, {3.748150572338011*^9, 
   3.7481506672736263`*^9}, {3.748150771651973*^9, 3.748150773533938*^9}, {
   3.748150852274338*^9, 3.7481508742086415`*^9}, 3.748150936952736*^9, {
   3.748150968513301*^9, 3.748151033207762*^9}, {3.748151228828043*^9, 
   3.748151236863692*^9}, {3.7481522941309853`*^9, 3.748152323817563*^9}, 
   3.7481523659319477`*^9, {3.7481524264081526`*^9, 3.7481524912786026`*^9}, 
   3.7481613464805307`*^9, {3.7481650976327305`*^9, 3.748165100926917*^9}, {
   3.748165141737867*^9, 3.748165230872306*^9}, {3.748165315381216*^9, 
   3.748165370630407*^9}, {3.7481654798023343`*^9, 3.7481654892610292`*^9}, {
   3.7481692578537617`*^9, 3.748169279295398*^9}, {3.7577686139902377`*^9, 
   3.7577687286774893`*^9}, {3.7577687765863495`*^9, 3.757768860909814*^9}, {
   3.75776889541652*^9, 3.7577689339594316`*^9}, {3.757769039007972*^9, 
   3.7577690630446844`*^9}, {3.757769135514849*^9, 3.7577691638001957`*^9}, {
   3.757769429067993*^9, 3.757769457226678*^9}, 3.757769587071046*^9, {
   3.7592154628239655`*^9, 3.759215499065191*^9}, {3.759215539906913*^9, 
   3.759215695690635*^9}, {3.759215731904752*^9, 3.7592157403083134`*^9}, {
   3.7592158199044504`*^9, 3.7592158652372065`*^9}, 3.7592159196237593`*^9, {
   3.75922311418956*^9, 3.7592231485436993`*^9}, {3.759223416714119*^9, 
   3.75922347955111*^9}, {3.7592236030667686`*^9, 3.7592237170728793`*^9}, {
   3.7592246081783752`*^9, 3.7592246107514944`*^9}, {3.759224659489154*^9, 
   3.759224759505679*^9}, 3.759225241164158*^9, {3.759225292492553*^9, 
   3.7592253062021246`*^9}, {3.7630869338898373`*^9, 3.763086991682808*^9}, {
   3.763087027860568*^9, 3.763087070334637*^9}, {3.7630871279595566`*^9, 
   3.7630871556715*^9}, {3.7630888329375415`*^9, 3.763088848924837*^9}, {
   3.7630888878258305`*^9, 3.763089082180278*^9}, {3.7630891540880146`*^9, 
   3.763089212329319*^9}, {3.7631578770906415`*^9, 3.763157891267444*^9}, {
   3.763158235331628*^9, 3.763158361001754*^9}, {3.7631584770106387`*^9, 
   3.7631584803367434`*^9}, {3.763158521905547*^9, 3.7631586564005947`*^9}, {
   3.763159575226506*^9, 3.7631596532663355`*^9}, {3.76315977807388*^9, 
   3.763159864517913*^9}, {3.763159953673379*^9, 3.7631600383258386`*^9}, {
   3.763160127503936*^9, 3.7631601764696608`*^9}, {3.763160877253928*^9, 
   3.7631609376861157`*^9}, {3.7631610153683643`*^9, 3.7631610155070333`*^9}, 
   3.7631614163516965`*^9, {3.763161503452248*^9, 3.7631615068918505`*^9}, {
   3.76316170941733*^9, 3.7631617718158064`*^9}, {3.7631618084669642`*^9, 
   3.7631619345489855`*^9}, {3.7631621772964535`*^9, 
   3.7631621945958157`*^9}, {3.7631622954758253`*^9, 
   3.7631623311752043`*^9}, {3.763162573095781*^9, 3.7631625810564933`*^9}, {
   3.763165007014879*^9, 3.7631650157624393`*^9}, {3.763165346894233*^9, 
   3.7631653592342196`*^9}, {3.7631654772141414`*^9, 3.763165490566574*^9}, {
   3.7631655277220955`*^9, 3.7631655926190104`*^9}, {3.7631656581316504`*^9, 
   3.763165704620087*^9}, {3.7631657544622936`*^9, 3.7631658412187023`*^9}, {
   3.7631659442558427`*^9, 3.7631659444143496`*^9}, {3.7631697399580326`*^9, 
   3.76316991533132*^9}, 3.7631699699656982`*^9, {3.763174351402421*^9, 
   3.763174353750779*^9}, {3.7631753037640495`*^9, 3.763175319861272*^9}, {
   3.7631753598098307`*^9, 3.763175371351607*^9}, {3.7631754061492767`*^9, 
   3.763175507092852*^9}, 3.763176110651868*^9, {3.763180564245925*^9, 
   3.7631805959987288`*^9}, {3.763180664242173*^9, 3.7631807171625504`*^9}, {
   3.7631846075493813`*^9, 3.7631847239337234`*^9}, {3.7632013082282653`*^9, 
   3.7632013622073803`*^9}, {3.763201395123904*^9, 3.7632013976278844`*^9}, {
   3.768724636461064*^9, 3.768724643103057*^9}, 3.7687247168880577`*^9, {
   3.7687259170417166`*^9, 3.768725966257715*^9}, {3.768733860636484*^9, 
   3.7687338660954847`*^9}, {3.768733912517484*^9, 3.768733934056484*^9}, {
   3.7858544277444243`*^9, 3.7858546060715413`*^9}, {3.78585467344009*^9, 
   3.785854708823527*^9}, {3.7858553315457616`*^9, 3.785855337641015*^9}, {
   3.785855368016358*^9, 3.785855420088813*^9}, {3.785855909025015*^9, 
   3.785856038063528*^9}, {3.785856088570183*^9, 3.7858561278955564`*^9}, {
   3.785856170002762*^9, 3.785856273233365*^9}, {3.7858563136099195`*^9, 
   3.785856313913683*^9}, {3.785856404692983*^9, 3.785856438530645*^9}, {
   3.7858565398177466`*^9, 3.7858565991205606`*^9}, {3.7858566668158393`*^9, 
   3.7858566880243216`*^9}, {3.7858567275705223`*^9, 
   3.7858567376037087`*^9}, {3.785857347559682*^9, 3.7858574179478493`*^9}, {
   3.7858584670428944`*^9, 3.7858585398252106`*^9}, {3.785858636962559*^9, 
   3.785858640522787*^9}, {3.785858670587372*^9, 3.785858712224944*^9}, {
   3.785858749458946*^9, 3.7858588420628247`*^9}, {3.7858590167141075`*^9, 
   3.7858590428887215`*^9}, {3.7858591191073675`*^9, 3.785859140713535*^9}, 
   3.785859215699136*^9, {3.7858592691705036`*^9, 3.7858592740956554`*^9}, {
   3.785859732487873*^9, 3.7858598203444495`*^9}, {3.785859858638613*^9, 
   3.7858600806077414`*^9}, {3.785860155552374*^9, 3.785860173446438*^9}, {
   3.785860557855685*^9, 3.7858605634063625`*^9}, {3.7858609358542967`*^9, 
   3.785860965302373*^9}, {3.7858610015861034`*^9, 3.785861002527371*^9}, {
   3.7858610335901794`*^9, 3.7858610480888867`*^9}, {3.785861310888216*^9, 
   3.78586134764559*^9}, {3.785861585945227*^9, 3.785861601189365*^9}, 
   3.785861639704359*^9, 3.785861782264332*^9, {3.7858626703013573`*^9, 
   3.7858627949033036`*^9}, 3.7858633369591446`*^9, 3.7858635901030107`*^9, {
   3.78586377259087*^9, 3.785863786465074*^9}, {3.7858638258953657`*^9, 
   3.785863832735037*^9}, {3.7858663769859962`*^9, 3.785866380252453*^9}, {
   3.785867314226081*^9, 3.7858673670049753`*^9}, {3.7858674157390213`*^9, 
   3.7858675183620973`*^9}, 3.786443521126769*^9, 3.7864435713766766`*^9, 
   3.786443660386431*^9, {3.786444574079462*^9, 3.786444669335345*^9}, {
   3.7864463001599927`*^9, 3.7864463036722603`*^9}, 3.786446419553109*^9, {
   3.786446461171731*^9, 3.786446477057373*^9}, {3.786446814881695*^9, 
   3.786446985519944*^9}, {3.7864470272095118`*^9, 3.786447057745755*^9}, {
   3.786447088912509*^9, 3.786447138648816*^9}, {3.786447193993759*^9, 
   3.786447250759598*^9}, {3.786449578316842*^9, 3.7864495891224365`*^9}, {
   3.786449644858076*^9, 3.786449684089555*^9}, {3.786450247122547*^9, 
   3.7864502531488476`*^9}, {3.7864503217215004`*^9, 
   3.7864503381697063`*^9}, {3.810694107588764*^9, 3.8106943923531904`*^9}, {
   3.8106944878209667`*^9, 3.8106945255132203`*^9}, {3.8106945849632916`*^9, 
   3.810694636317973*^9}, {3.810694771994443*^9, 3.81069490393817*^9}, {
   3.810694938731064*^9, 3.8106949735321035`*^9}, {3.8106950611797037`*^9, 
   3.810695089166856*^9}, 3.8106953732763147`*^9, {3.8106954209508605`*^9, 
   3.8106954262496953`*^9}, 3.8106954611344547`*^9, {3.810695501560954*^9, 
   3.810695523032544*^9}, {3.810695583669401*^9, 3.810695628347964*^9}, {
   3.810695660409269*^9, 3.810695704152301*^9}, {3.810696116031282*^9, 
   3.8106961198799925`*^9}, {3.8106962219404044`*^9, 3.810696242808605*^9}, {
   3.8106964753200064`*^9, 3.810696477209955*^9}, {3.8106965597333355`*^9, 
   3.8106965663725867`*^9}, {3.8106966443032484`*^9, 3.810696647206484*^9}, {
   3.810722503608433*^9, 3.8107226654936476`*^9}, {3.81072311533906*^9, 
   3.8107231534631042`*^9}, {3.812589210352528*^9, 3.812589304446389*^9}, {
   3.8125893719424047`*^9, 3.812589478501624*^9}, {3.812589587856048*^9, 
   3.8125896038647747`*^9}, {3.8126325503437624`*^9, 
   3.8126326014195514`*^9}, {3.8128549686842012`*^9, 
   3.8128549687941356`*^9}, {3.8130451620035343`*^9, 3.813045169889459*^9}, {
   3.8183206087977695`*^9, 3.8183206354952345`*^9}, 3.8324070270285006`*^9, {
   3.832407072973501*^9, 3.8324070819324875`*^9}, {3.8324071434792604`*^9, 
   3.832407170913245*^9}, {3.8324105153610115`*^9, 3.8324105153650317`*^9}, 
   3.838988147274657*^9, {3.838988179043666*^9, 3.8389883524186716`*^9}, {
   3.838988629206687*^9, 3.8389887410826874`*^9}, {3.8389891327497053`*^9, 
   3.8389891448440456`*^9}, {3.8389903425353055`*^9, 
   3.8389903435562997`*^9}, {3.838990427837316*^9, 3.8389904450456104`*^9}, {
   3.8389907252536163`*^9, 3.8389907304886084`*^9}, 3.8389913212066746`*^9, 
   3.8390331030290174`*^9, {3.839165620600835*^9, 3.8391659575340805`*^9}, {
   3.8391660164610844`*^9, 3.8391660188050685`*^9}, 3.839166062799084*^9, {
   3.8391662983983617`*^9, 3.8391663039900455`*^9}, {3.839166401157569*^9, 
   3.8391664260295563`*^9}, {3.8391664563985825`*^9, 
   3.8391665271660643`*^9}, {3.8391673683469543`*^9, 3.839167466926094*^9}, {
   3.839167503500153*^9, 3.8391675370714703`*^9}, {3.8391676169762554`*^9, 
   3.839167680708274*^9}, {3.839167731943289*^9, 3.839167749519197*^9}, {
   3.8391680031859474`*^9, 3.8391680083239393`*^9}, {3.839168051575951*^9, 
   3.8391680531959686`*^9}, {3.839168088051008*^9, 3.839168094135991*^9}, {
   3.8391682769846787`*^9, 3.839168337080731*^9}, {3.8391683904997106`*^9, 
   3.839168413175714*^9}, 3.83916864397909*^9, {3.8391686750875587`*^9, 
   3.839168714428542*^9}, {3.8391687469465594`*^9, 3.8391687507245626`*^9}, {
   3.839168834464542*^9, 3.839168866290809*^9}, {3.839168899946811*^9, 
   3.839168922712819*^9}, {3.839168968035813*^9, 3.839168970567823*^9}, {
   3.839169045359809*^9, 3.839169085600784*^9}, {3.839169302290578*^9, 
   3.8391693265371494`*^9}, {3.839169708175756*^9, 3.8391697127087555`*^9}, {
   3.8391697804358563`*^9, 3.8391697819948587`*^9}, {3.8391699731712875`*^9, 
   3.8391699852412877`*^9}, {3.839170208717842*^9, 3.839170219182282*^9}, {
   3.839170569174945*^9, 3.839170577170945*^9}, {3.839170960551553*^9, 
   3.8391709629815516`*^9}, 3.839171888118546*^9, {3.839172834882839*^9, 
   3.8391728751787214`*^9}, {3.8391730062107773`*^9, 3.839173024134774*^9}, {
   3.8391732486748257`*^9, 3.83917325438282*^9}, {3.8391734389317517`*^9, 
   3.8391734904747524`*^9}, {3.8391738488822227`*^9, 
   3.8391738699239254`*^9}, {3.839174277173421*^9, 3.8391742829554214`*^9}, {
   3.8391743337244053`*^9, 3.839174366112199*^9}, 3.8391744412642336`*^9, {
   3.8391751005682554`*^9, 3.839175113124239*^9}, {3.8391751808042545`*^9, 
   3.839175356303198*^9}, {3.839175392477195*^9, 3.8391754223611984`*^9}, {
   3.839175456078521*^9, 3.83917548020552*^9}, {3.8391755729175253`*^9, 
   3.839175601405748*^9}, {3.8391756386068335`*^9, 3.8391756412938533`*^9}, {
   3.839175820080815*^9, 3.839175864504131*^9}, {3.8391766319743986`*^9, 
   3.8391766749093227`*^9}, {3.8391777077597523`*^9, 
   3.8391777572487907`*^9}, {3.8391777898617983`*^9, 3.83917779509778*^9}, {
   3.8391800897127852`*^9, 3.83918012595477*^9}, {3.8394292410523396`*^9, 
   3.839429266612468*^9}, {3.839429368602217*^9, 3.8394293833313074`*^9}, {
   3.8396233767708187`*^9, 3.8396233831651483`*^9}, 3.839623671013212*^9, {
   3.8396509030708003`*^9, 3.839650912030799*^9}, {3.8396737646001205`*^9, 
   3.839673820319213*^9}, 3.8396738576482124`*^9, {3.8396738883372126`*^9, 
   3.839673985993554*^9}, {3.83967402452347*^9, 3.8396740674693737`*^9}, {
   3.839680551274977*^9, 3.8396806380408025`*^9}, {3.8397256737049084`*^9, 
   3.8397257951619167`*^9}, {3.8397258384114995`*^9, 3.8397258442794914`*^9}, 
   3.8397258871007643`*^9, {3.8397277995082555`*^9, 3.8397278024753666`*^9}, {
   3.8397281983097134`*^9, 3.839728307752576*^9}, {3.8397536944901733`*^9, 
   3.839753714838767*^9}, 3.8397540223398185`*^9, {3.839755624874116*^9, 
   3.839755649426776*^9}, {3.83975995627477*^9, 3.8397601780268793`*^9}, {
   3.8402946774559727`*^9, 3.8402946876440077`*^9}, {3.8403500929920244`*^9, 
   3.840350102248304*^9}, {3.8404440390821543`*^9, 3.840444130756686*^9}, {
   3.840444178620683*^9, 3.8404441870951614`*^9}, {3.8404442866757402`*^9, 
   3.8404443186846547`*^9}, {3.840444473837395*^9, 3.8404444797743835`*^9}, {
   3.840444605353613*^9, 3.8404446076356106`*^9}, {3.8404448691255684`*^9, 
   3.8404448792929335`*^9}, {3.840446323640649*^9, 3.840446329573303*^9}, {
   3.8404481898864784`*^9, 3.8404481906412425`*^9}, {3.840465183543213*^9, 
   3.8404652469817314`*^9}, {3.840491425134797*^9, 3.840491445163833*^9}, {
   3.840491475983799*^9, 3.8404915502748346`*^9}, {3.8404915939047995`*^9, 
   3.840491599955798*^9}, {3.8404916357798004`*^9, 3.8404916435127993`*^9}, {
   3.8406819560517597`*^9, 3.840682119936493*^9}, {3.8406821723675065`*^9, 
   3.8406822080434923`*^9}, {3.840682365653475*^9, 3.840682473196146*^9}, {
   3.840682515458133*^9, 3.8406825398181343`*^9}, {3.8406826857875175`*^9, 
   3.840682688152525*^9}, {3.8406827201145177`*^9, 3.840682768446001*^9}, {
   3.8406831943520603`*^9, 3.8406832826385083`*^9}, 3.8406834034790077`*^9},
 CellLabel->
  "In[5340]:=",ExpressionUUID->"1874d45f-36c8-481d-a96c-727d8c067141"],

Cell[CellGroupData[{

Cell[BoxData[
 InterpretationBox[
  RowBox[{"\<\"A=\"\>", "\[InvisibleSpace]", 
   TagBox[
    RowBox[{"(", "\[NoBreak]", GridBox[{
       {
        RowBox[{
         RowBox[{"-", "r"}], " ", 
         RowBox[{"Cos", "[", "\[Theta]", "]"}], " ", 
         RowBox[{"Sin", "[", "\[Lambda]", "]"}]}], 
        RowBox[{
         RowBox[{"-", "r"}], " ", 
         RowBox[{"Cos", "[", "\[Lambda]", "]"}], " ", 
         RowBox[{"Sin", "[", "\[Theta]", "]"}]}], 
        RowBox[{
         RowBox[{"Cos", "[", "\[Theta]", "]"}], " ", 
         RowBox[{"Cos", "[", "\[Lambda]", "]"}]}]},
       {
        RowBox[{"r", " ", 
         RowBox[{"Cos", "[", "\[Theta]", "]"}], " ", 
         RowBox[{"Cos", "[", "\[Lambda]", "]"}]}], 
        RowBox[{
         RowBox[{"-", "r"}], " ", 
         RowBox[{"Sin", "[", "\[Theta]", "]"}], " ", 
         RowBox[{"Sin", "[", "\[Lambda]", "]"}]}], 
        RowBox[{
         RowBox[{"Cos", "[", "\[Theta]", "]"}], " ", 
         RowBox[{"Sin", "[", "\[Lambda]", "]"}]}]},
       {"0", 
        RowBox[{"r", " ", 
         RowBox[{"Cos", "[", "\[Theta]", "]"}]}], 
        RowBox[{"Sin", "[", "\[Theta]", "]"}]}
      },
      GridBoxAlignment->{
       "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
        "Rows" -> {{Baseline}}, "RowsIndexed" -> {}},
      GridBoxSpacings->{"Columns" -> {
          Offset[0.27999999999999997`], {
           Offset[0.7]}, 
          Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
          Offset[0.2], {
           Offset[0.4]}, 
          Offset[0.2]}, "RowsIndexed" -> {}}], "\[NoBreak]", ")"}],
    Function[BoxForm`e$, 
     MatrixForm[BoxForm`e$]]]}],
  SequenceForm["A=", 
   MatrixForm[{{-$CellContext`r Cos[$CellContext`\[Theta]] 
      Sin[$CellContext`\[Lambda]], -$CellContext`r 
      Cos[$CellContext`\[Lambda]] Sin[$CellContext`\[Theta]], 
      Cos[$CellContext`\[Theta]] 
      Cos[$CellContext`\[Lambda]]}, {$CellContext`r 
      Cos[$CellContext`\[Theta]] Cos[$CellContext`\[Lambda]], -$CellContext`r 
      Sin[$CellContext`\[Theta]] Sin[$CellContext`\[Lambda]], 
      Cos[$CellContext`\[Theta]] Sin[$CellContext`\[Lambda]]}, {
     0, $CellContext`r Cos[$CellContext`\[Theta]], 
      Sin[$CellContext`\[Theta]]}}]],
  Editable->False]], "Print",
 CellChangeTimes->{
  3.840682341599472*^9, {3.8406823792085066`*^9, 3.840682389413476*^9}, {
   3.8406824654121337`*^9, 3.840682475116167*^9}, {3.840682541628132*^9, 
   3.840682567239843*^9}, {3.8406832010910625`*^9, 3.840683277649497*^9}, 
   3.8406833568807435`*^9, 3.8406834053790116`*^9},
 CellLabel->
  "\:6b63\:5728\:8ba1\:7b97In[5340]:=",ExpressionUUID->"7ecd8500-03a8-40bd-\
822f-895453990cd9"],

Cell[BoxData[
 InterpretationBox[
  RowBox[{"\<\"iA=\"\>", "\[InvisibleSpace]", 
   TagBox[
    RowBox[{"(", "\[NoBreak]", GridBox[{
       {
        RowBox[{"-", 
         FractionBox[
          RowBox[{
           RowBox[{"Sec", "[", "\[Theta]", "]"}], " ", 
           RowBox[{"Sin", "[", "\[Lambda]", "]"}]}], "r"]}], 
        FractionBox[
         RowBox[{
          RowBox[{"Cos", "[", "\[Lambda]", "]"}], " ", 
          RowBox[{"Sec", "[", "\[Theta]", "]"}]}], "r"], "0"},
       {
        RowBox[{"-", 
         FractionBox[
          RowBox[{
           RowBox[{"Cos", "[", "\[Lambda]", "]"}], " ", 
           RowBox[{"Sin", "[", "\[Theta]", "]"}]}], "r"]}], 
        RowBox[{"-", 
         FractionBox[
          RowBox[{
           RowBox[{"Sin", "[", "\[Theta]", "]"}], " ", 
           RowBox[{"Sin", "[", "\[Lambda]", "]"}]}], "r"]}], 
        FractionBox[
         RowBox[{"Cos", "[", "\[Theta]", "]"}], "r"]},
       {
        RowBox[{
         RowBox[{"Cos", "[", "\[Theta]", "]"}], " ", 
         RowBox[{"Cos", "[", "\[Lambda]", "]"}]}], 
        RowBox[{
         RowBox[{"Cos", "[", "\[Theta]", "]"}], " ", 
         RowBox[{"Sin", "[", "\[Lambda]", "]"}]}], 
        RowBox[{"Sin", "[", "\[Theta]", "]"}]}
      },
      GridBoxAlignment->{
       "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
        "Rows" -> {{Baseline}}, "RowsIndexed" -> {}},
      GridBoxSpacings->{"Columns" -> {
          Offset[0.27999999999999997`], {
           Offset[0.7]}, 
          Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
          Offset[0.2], {
           Offset[0.4]}, 
          Offset[0.2]}, "RowsIndexed" -> {}}], "\[NoBreak]", ")"}],
    Function[BoxForm`e$, 
     MatrixForm[BoxForm`e$]]]}],
  SequenceForm["iA=", 
   MatrixForm[{{-$CellContext`r^(-1) Sec[$CellContext`\[Theta]] 
      Sin[$CellContext`\[Lambda]], $CellContext`r^(-1) 
      Cos[$CellContext`\[Lambda]] Sec[$CellContext`\[Theta]], 
      0}, {-$CellContext`r^(-1) Cos[$CellContext`\[Lambda]] 
      Sin[$CellContext`\[Theta]], -$CellContext`r^(-1) 
      Sin[$CellContext`\[Theta]] 
      Sin[$CellContext`\[Lambda]], $CellContext`r^(-1) 
      Cos[$CellContext`\[Theta]]}, {
     Cos[$CellContext`\[Theta]] Cos[$CellContext`\[Lambda]], 
      Cos[$CellContext`\[Theta]] Sin[$CellContext`\[Lambda]], 
      Sin[$CellContext`\[Theta]]}}]],
  Editable->False]], "Print",
 CellChangeTimes->{
  3.840682341599472*^9, {3.8406823792085066`*^9, 3.840682389413476*^9}, {
   3.8406824654121337`*^9, 3.840682475116167*^9}, {3.840682541628132*^9, 
   3.840682567239843*^9}, {3.8406832010910625`*^9, 3.840683277649497*^9}, 
   3.8406833568807435`*^9, 3.8406834053860407`*^9},
 CellLabel->
  "\:6b63\:5728\:8ba1\:7b97In[5340]:=",ExpressionUUID->"9b424bb9-0d57-4114-\
bd37-3c837216830e"],

Cell[BoxData[
 InterpretationBox[
  RowBox[{"\<\"G=\"\>", "\[InvisibleSpace]", 
   TagBox[
    RowBox[{"(", "\[NoBreak]", GridBox[{
       {
        RowBox[{
         SuperscriptBox["r", "2"], " ", 
         SuperscriptBox[
          RowBox[{"Cos", "[", "\[Theta]", "]"}], "2"]}], "0", "0"},
       {"0", 
        SuperscriptBox["r", "2"], "0"},
       {"0", "0", "1"}
      },
      GridBoxAlignment->{
       "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
        "Rows" -> {{Baseline}}, "RowsIndexed" -> {}},
      GridBoxSpacings->{"Columns" -> {
          Offset[0.27999999999999997`], {
           Offset[0.7]}, 
          Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
          Offset[0.2], {
           Offset[0.4]}, 
          Offset[0.2]}, "RowsIndexed" -> {}}], "\[NoBreak]", ")"}],
    Function[BoxForm`e$, 
     MatrixForm[BoxForm`e$]]]}],
  SequenceForm["G=", 
   MatrixForm[{{$CellContext`r^2 Cos[$CellContext`\[Theta]]^2, 0, 0}, {
     0, $CellContext`r^2, 0}, {0, 0, 1}}]],
  Editable->False]], "Print",
 CellChangeTimes->{
  3.840682341599472*^9, {3.8406823792085066`*^9, 3.840682389413476*^9}, {
   3.8406824654121337`*^9, 3.840682475116167*^9}, {3.840682541628132*^9, 
   3.840682567239843*^9}, {3.8406832010910625`*^9, 3.840683277649497*^9}, 
   3.8406833568807435`*^9, 3.840683405400036*^9},
 CellLabel->
  "\:6b63\:5728\:8ba1\:7b97In[5340]:=",ExpressionUUID->"f3e36976-75d4-4a46-\
b3ce-dd4c20474e28"],

Cell[BoxData[
 InterpretationBox[
  RowBox[{"\<\"iG=\"\>", "\[InvisibleSpace]", 
   TagBox[
    RowBox[{"(", "\[NoBreak]", GridBox[{
       {
        FractionBox[
         SuperscriptBox[
          RowBox[{"Sec", "[", "\[Theta]", "]"}], "2"], 
         SuperscriptBox["r", "2"]], "0", "0"},
       {"0", 
        FractionBox["1", 
         SuperscriptBox["r", "2"]], "0"},
       {"0", "0", "1"}
      },
      GridBoxAlignment->{
       "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
        "Rows" -> {{Baseline}}, "RowsIndexed" -> {}},
      GridBoxSpacings->{"Columns" -> {
          Offset[0.27999999999999997`], {
           Offset[0.7]}, 
          Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
          Offset[0.2], {
           Offset[0.4]}, 
          Offset[0.2]}, "RowsIndexed" -> {}}], "\[NoBreak]", ")"}],
    Function[BoxForm`e$, 
     MatrixForm[BoxForm`e$]]]}],
  SequenceForm["iG=", 
   MatrixForm[{{$CellContext`r^(-2) Sec[$CellContext`\[Theta]]^2, 0, 0}, {
     0, $CellContext`r^(-2), 0}, {0, 0, 1}}]],
  Editable->False]], "Print",
 CellChangeTimes->{
  3.840682341599472*^9, {3.8406823792085066`*^9, 3.840682389413476*^9}, {
   3.8406824654121337`*^9, 3.840682475116167*^9}, {3.840682541628132*^9, 
   3.840682567239843*^9}, {3.8406832010910625`*^9, 3.840683277649497*^9}, 
   3.8406833568807435`*^9, 3.8406834054040356`*^9},
 CellLabel->
  "\:6b63\:5728\:8ba1\:7b97In[5340]:=",ExpressionUUID->"0aef69e6-f01e-48af-\
82a1-f68dbfca13bb"],

Cell[BoxData[
 InterpretationBox[
  RowBox[{"\<\"sqrtG=\"\>", "\[InvisibleSpace]", 
   RowBox[{
    SuperscriptBox["r", "2"], " ", 
    SqrtBox[
     SuperscriptBox[
      RowBox[{"Cos", "[", "\[Theta]", "]"}], "2"]]}]}],
  SequenceForm[
  "sqrtG=", $CellContext`r^2 (Cos[$CellContext`\[Theta]]^2)^Rational[1, 2]],
  Editable->False]], "Print",
 CellChangeTimes->{
  3.840682341599472*^9, {3.8406823792085066`*^9, 3.840682389413476*^9}, {
   3.8406824654121337`*^9, 3.840682475116167*^9}, {3.840682541628132*^9, 
   3.840682567239843*^9}, {3.8406832010910625`*^9, 3.840683277649497*^9}, 
   3.8406833568807435`*^9, 3.8406834054110355`*^9},
 CellLabel->
  "\:6b63\:5728\:8ba1\:7b97In[5340]:=",ExpressionUUID->"c0bcd2c6-29ae-44ec-\
9683-6cd87e7c7ccc"],

Cell[BoxData[
 InterpretationBox[
  RowBox[{"\<\"dGdlon=\"\>", "\[InvisibleSpace]", 
   TagBox[
    RowBox[{"(", "\[NoBreak]", GridBox[{
       {"0", "0", "0"},
       {"0", "0", "0"},
       {"0", "0", "0"}
      },
      GridBoxAlignment->{
       "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
        "Rows" -> {{Baseline}}, "RowsIndexed" -> {}},
      GridBoxSpacings->{"Columns" -> {
          Offset[0.27999999999999997`], {
           Offset[0.7]}, 
          Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
          Offset[0.2], {
           Offset[0.4]}, 
          Offset[0.2]}, "RowsIndexed" -> {}}], "\[NoBreak]", ")"}],
    Function[BoxForm`e$, 
     MatrixForm[BoxForm`e$]]]}],
  SequenceForm["dGdlon=", 
   MatrixForm[{{0, 0, 0}, {0, 0, 0}, {0, 0, 0}}]],
  Editable->False]], "Print",
 CellChangeTimes->{
  3.840682341599472*^9, {3.8406823792085066`*^9, 3.840682389413476*^9}, {
   3.8406824654121337`*^9, 3.840682475116167*^9}, {3.840682541628132*^9, 
   3.840682567239843*^9}, {3.8406832010910625`*^9, 3.840683277649497*^9}, 
   3.8406833568807435`*^9, 3.840683405415032*^9},
 CellLabel->
  "\:6b63\:5728\:8ba1\:7b97In[5340]:=",ExpressionUUID->"306517af-c0ec-467f-\
8122-2e5eaf549686"],

Cell[BoxData[
 InterpretationBox[
  RowBox[{"\<\"dGdlat=\"\>", "\[InvisibleSpace]", 
   TagBox[
    RowBox[{"(", "\[NoBreak]", GridBox[{
       {
        RowBox[{
         RowBox[{"-", "2"}], " ", 
         SuperscriptBox["r", "2"], " ", 
         RowBox[{"Cos", "[", "\[Theta]", "]"}], " ", 
         RowBox[{"Sin", "[", "\[Theta]", "]"}]}], "0", "0"},
       {"0", "0", "0"},
       {"0", "0", "0"}
      },
      GridBoxAlignment->{
       "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
        "Rows" -> {{Baseline}}, "RowsIndexed" -> {}},
      GridBoxSpacings->{"Columns" -> {
          Offset[0.27999999999999997`], {
           Offset[0.7]}, 
          Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
          Offset[0.2], {
           Offset[0.4]}, 
          Offset[0.2]}, "RowsIndexed" -> {}}], "\[NoBreak]", ")"}],
    Function[BoxForm`e$, 
     MatrixForm[BoxForm`e$]]]}],
  SequenceForm["dGdlat=", 
   MatrixForm[{{(-2) $CellContext`r^2 Cos[$CellContext`\[Theta]] 
      Sin[$CellContext`\[Theta]], 0, 0}, {0, 0, 0}, {0, 0, 0}}]],
  Editable->False]], "Print",
 CellChangeTimes->{
  3.840682341599472*^9, {3.8406823792085066`*^9, 3.840682389413476*^9}, {
   3.8406824654121337`*^9, 3.840682475116167*^9}, {3.840682541628132*^9, 
   3.840682567239843*^9}, {3.8406832010910625`*^9, 3.840683277649497*^9}, 
   3.8406833568807435`*^9, 3.840683405419041*^9},
 CellLabel->
  "\:6b63\:5728\:8ba1\:7b97In[5340]:=",ExpressionUUID->"a739d458-08c7-46fe-\
b233-96720ac7e606"],

Cell[BoxData[
 InterpretationBox[
  RowBox[{"\<\"dGdr=\"\>", "\[InvisibleSpace]", 
   TagBox[
    RowBox[{"(", "\[NoBreak]", GridBox[{
       {
        RowBox[{"2", " ", "r", " ", 
         SuperscriptBox[
          RowBox[{"Cos", "[", "\[Theta]", "]"}], "2"]}], "0", "0"},
       {"0", 
        RowBox[{"2", " ", "r"}], "0"},
       {"0", "0", "0"}
      },
      GridBoxAlignment->{
       "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
        "Rows" -> {{Baseline}}, "RowsIndexed" -> {}},
      GridBoxSpacings->{"Columns" -> {
          Offset[0.27999999999999997`], {
           Offset[0.7]}, 
          Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
          Offset[0.2], {
           Offset[0.4]}, 
          Offset[0.2]}, "RowsIndexed" -> {}}], "\[NoBreak]", ")"}],
    Function[BoxForm`e$, 
     MatrixForm[BoxForm`e$]]]}],
  SequenceForm["dGdr=", 
   MatrixForm[{{2 $CellContext`r Cos[$CellContext`\[Theta]]^2, 0, 0}, {
     0, 2 $CellContext`r, 0}, {0, 0, 0}}]],
  Editable->False]], "Print",
 CellChangeTimes->{
  3.840682341599472*^9, {3.8406823792085066`*^9, 3.840682389413476*^9}, {
   3.8406824654121337`*^9, 3.840682475116167*^9}, {3.840682541628132*^9, 
   3.840682567239843*^9}, {3.8406832010910625`*^9, 3.840683277649497*^9}, 
   3.8406833568807435`*^9, 3.840683405428008*^9},
 CellLabel->
  "\:6b63\:5728\:8ba1\:7b97In[5340]:=",ExpressionUUID->"ecd7aee2-f71d-424e-\
a11b-2256dbac52c8"],

Cell[BoxData[
 InterpretationBox[
  RowBox[{"\<\"Christoffel=\"\>", "\[InvisibleSpace]", 
   TagBox[
    RowBox[{"(", "\[NoBreak]", GridBox[{
       {
        RowBox[{"(", "\[NoBreak]", 
         TagBox[GridBox[{
            {"0"},
            {
             RowBox[{"-", 
              RowBox[{"Tan", "[", "\[Theta]", "]"}]}]},
            {
             FractionBox["1", "r"]}
           },
           
           GridBoxAlignment->{
            "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
             "Rows" -> {{Baseline}}, "RowsIndexed" -> {}},
           GridBoxSpacings->{"Columns" -> {
               Offset[0.27999999999999997`], {
                Offset[0.5599999999999999]}, 
               Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
               Offset[0.2], {
                Offset[0.4]}, 
               Offset[0.2]}, "RowsIndexed" -> {}}],
          Column], "\[NoBreak]", ")"}], 
        RowBox[{"(", "\[NoBreak]", 
         TagBox[GridBox[{
            {
             RowBox[{"-", 
              RowBox[{"Tan", "[", "\[Theta]", "]"}]}]},
            {"0"},
            {"0"}
           },
           
           GridBoxAlignment->{
            "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
             "Rows" -> {{Baseline}}, "RowsIndexed" -> {}},
           GridBoxSpacings->{"Columns" -> {
               Offset[0.27999999999999997`], {
                Offset[0.5599999999999999]}, 
               Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
               Offset[0.2], {
                Offset[0.4]}, 
               Offset[0.2]}, "RowsIndexed" -> {}}],
          Column], "\[NoBreak]", ")"}], 
        RowBox[{"(", "\[NoBreak]", 
         TagBox[GridBox[{
            {
             FractionBox["1", "r"]},
            {"0"},
            {"0"}
           },
           
           GridBoxAlignment->{
            "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
             "Rows" -> {{Baseline}}, "RowsIndexed" -> {}},
           GridBoxSpacings->{"Columns" -> {
               Offset[0.27999999999999997`], {
                Offset[0.5599999999999999]}, 
               Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
               Offset[0.2], {
                Offset[0.4]}, 
               Offset[0.2]}, "RowsIndexed" -> {}}],
          Column], "\[NoBreak]", ")"}]},
       {
        RowBox[{"(", "\[NoBreak]", 
         TagBox[GridBox[{
            {
             RowBox[{
              RowBox[{"Cos", "[", "\[Theta]", "]"}], " ", 
              RowBox[{"Sin", "[", "\[Theta]", "]"}]}]},
            {"0"},
            {"0"}
           },
           
           GridBoxAlignment->{
            "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
             "Rows" -> {{Baseline}}, "RowsIndexed" -> {}},
           GridBoxSpacings->{"Columns" -> {
               Offset[0.27999999999999997`], {
                Offset[0.5599999999999999]}, 
               Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
               Offset[0.2], {
                Offset[0.4]}, 
               Offset[0.2]}, "RowsIndexed" -> {}}],
          Column], "\[NoBreak]", ")"}], 
        RowBox[{"(", "\[NoBreak]", 
         TagBox[GridBox[{
            {"0"},
            {"0"},
            {
             FractionBox["1", "r"]}
           },
           
           GridBoxAlignment->{
            "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
             "Rows" -> {{Baseline}}, "RowsIndexed" -> {}},
           GridBoxSpacings->{"Columns" -> {
               Offset[0.27999999999999997`], {
                Offset[0.5599999999999999]}, 
               Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
               Offset[0.2], {
                Offset[0.4]}, 
               Offset[0.2]}, "RowsIndexed" -> {}}],
          Column], "\[NoBreak]", ")"}], 
        RowBox[{"(", "\[NoBreak]", 
         TagBox[GridBox[{
            {"0"},
            {
             FractionBox["1", "r"]},
            {"0"}
           },
           
           GridBoxAlignment->{
            "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
             "Rows" -> {{Baseline}}, "RowsIndexed" -> {}},
           GridBoxSpacings->{"Columns" -> {
               Offset[0.27999999999999997`], {
                Offset[0.5599999999999999]}, 
               Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
               Offset[0.2], {
                Offset[0.4]}, 
               Offset[0.2]}, "RowsIndexed" -> {}}],
          Column], "\[NoBreak]", ")"}]},
       {
        RowBox[{"(", "\[NoBreak]", 
         TagBox[GridBox[{
            {
             RowBox[{
              RowBox[{"-", "r"}], " ", 
              SuperscriptBox[
               RowBox[{"Cos", "[", "\[Theta]", "]"}], "2"]}]},
            {"0"},
            {"0"}
           },
           
           GridBoxAlignment->{
            "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
             "Rows" -> {{Baseline}}, "RowsIndexed" -> {}},
           GridBoxSpacings->{"Columns" -> {
               Offset[0.27999999999999997`], {
                Offset[0.5599999999999999]}, 
               Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
               Offset[0.2], {
                Offset[0.4]}, 
               Offset[0.2]}, "RowsIndexed" -> {}}],
          Column], "\[NoBreak]", ")"}], 
        RowBox[{"(", "\[NoBreak]", 
         TagBox[GridBox[{
            {"0"},
            {
             RowBox[{"-", "r"}]},
            {"0"}
           },
           
           GridBoxAlignment->{
            "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
             "Rows" -> {{Baseline}}, "RowsIndexed" -> {}},
           GridBoxSpacings->{"Columns" -> {
               Offset[0.27999999999999997`], {
                Offset[0.5599999999999999]}, 
               Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
               Offset[0.2], {
                Offset[0.4]}, 
               Offset[0.2]}, "RowsIndexed" -> {}}],
          Column], "\[NoBreak]", ")"}], 
        RowBox[{"(", "\[NoBreak]", 
         TagBox[GridBox[{
            {"0"},
            {"0"},
            {"0"}
           },
           
           GridBoxAlignment->{
            "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
             "Rows" -> {{Baseline}}, "RowsIndexed" -> {}},
           GridBoxSpacings->{"Columns" -> {
               Offset[0.27999999999999997`], {
                Offset[0.5599999999999999]}, 
               Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
               Offset[0.2], {
                Offset[0.4]}, 
               Offset[0.2]}, "RowsIndexed" -> {}}],
          Column], "\[NoBreak]", ")"}]}
      },
      GridBoxAlignment->{
       "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
        "Rows" -> {{Baseline}}, "RowsIndexed" -> {}},
      GridBoxSpacings->{"Columns" -> {
          Offset[0.27999999999999997`], {
           Offset[0.7]}, 
          Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
          Offset[0.2], {
           Offset[0.4]}, 
          Offset[0.2]}, "RowsIndexed" -> {}}], "\[NoBreak]", ")"}],
    Function[BoxForm`e$, 
     MatrixForm[BoxForm`e$]]]}],
  SequenceForm["Christoffel=", 
   MatrixForm[{{{
      0, -Tan[$CellContext`\[Theta]], $CellContext`r^(-1)}, {-
       Tan[$CellContext`\[Theta]], 0, 0}, {$CellContext`r^(-1), 0, 0}}, {{
      Cos[$CellContext`\[Theta]] Sin[$CellContext`\[Theta]], 0, 0}, {
      0, 0, $CellContext`r^(-1)}, {
      0, $CellContext`r^(-1), 0}}, {{-$CellContext`r 
       Cos[$CellContext`\[Theta]]^2, 0, 0}, {0, -$CellContext`r, 0}, {0, 0, 
      0}}}]],
  Editable->False]], "Print",
 CellChangeTimes->{
  3.840682341599472*^9, {3.8406823792085066`*^9, 3.840682389413476*^9}, {
   3.8406824654121337`*^9, 3.840682475116167*^9}, {3.840682541628132*^9, 
   3.840682567239843*^9}, {3.8406832010910625`*^9, 3.840683277649497*^9}, 
   3.8406833568807435`*^9, 3.8406834054380093`*^9},
 CellLabel->
  "\:6b63\:5728\:8ba1\:7b97In[5340]:=",ExpressionUUID->"a59aaab7-2291-489a-\
aa3b-eb225bffca07"]
}, Open  ]],

Cell[BoxData["0"], "Output",
 CellChangeTimes->{
  3.8406823416644735`*^9, {3.840682379261511*^9, 3.8406823894754925`*^9}, {
   3.840682465476153*^9, 3.8406824751781683`*^9}, {3.8406825416851673`*^9, 
   3.840682567301887*^9}, {3.8406832011680574`*^9, 3.840683277707505*^9}, 
   3.8406833569667234`*^9, 3.840683405449008*^9},
 CellLabel->
  "Out[5376]=",ExpressionUUID->"fdd62302-3f66-4f67-b93e-e37807033b6c"],

Cell[BoxData[
 RowBox[{"\[Omega]", " ", 
  RowBox[{"Cos", "[", "\[Theta]", "]"}]}]], "Output",
 CellChangeTimes->{
  3.8406823416644735`*^9, {3.840682379261511*^9, 3.8406823894754925`*^9}, {
   3.840682465476153*^9, 3.8406824751781683`*^9}, {3.8406825416851673`*^9, 
   3.840682567301887*^9}, {3.8406832011680574`*^9, 3.840683277707505*^9}, 
   3.8406833569667234`*^9, 3.8406834054530063`*^9},
 CellLabel->
  "Out[5377]=",ExpressionUUID->"3a7a9d05-1f44-42a0-8952-928e3b75d339"],

Cell[BoxData[
 RowBox[{"\[Omega]", " ", 
  RowBox[{"Sin", "[", "\[Theta]", "]"}]}]], "Output",
 CellChangeTimes->{
  3.8406823416644735`*^9, {3.840682379261511*^9, 3.8406823894754925`*^9}, {
   3.840682465476153*^9, 3.8406824751781683`*^9}, {3.8406825416851673`*^9, 
   3.840682567301887*^9}, {3.8406832011680574`*^9, 3.840683277707505*^9}, 
   3.8406833569667234`*^9, 3.84068340545601*^9},
 CellLabel->
  "Out[5378]=",ExpressionUUID->"b8fa54e7-534e-40d8-bcd2-bfe3a0f64ac4"],

Cell[BoxData["0"], "Output",
 CellChangeTimes->{
  3.8406823416644735`*^9, {3.840682379261511*^9, 3.8406823894754925`*^9}, {
   3.840682465476153*^9, 3.8406824751781683`*^9}, {3.8406825416851673`*^9, 
   3.840682567301887*^9}, {3.8406832011680574`*^9, 3.840683277707505*^9}, 
   3.8406833569667234`*^9, 3.8406834054620314`*^9},
 CellLabel->
  "Out[5381]=",ExpressionUUID->"3e7ffcc0-9438-4e2d-b432-2c178b37c05f"],

Cell[BoxData[
 RowBox[{
  RowBox[{"-", 
   SuperscriptBox["\[Omega]", "2"]}], " ", 
  RowBox[{"Sin", "[", "\[Theta]", "]"}]}]], "Output",
 CellChangeTimes->{
  3.8406823416644735`*^9, {3.840682379261511*^9, 3.8406823894754925`*^9}, {
   3.840682465476153*^9, 3.8406824751781683`*^9}, {3.8406825416851673`*^9, 
   3.840682567301887*^9}, {3.8406832011680574`*^9, 3.840683277707505*^9}, 
   3.8406833569667234`*^9, 3.840683405465041*^9},
 CellLabel->
  "Out[5382]=",ExpressionUUID->"57b40b92-01df-4de0-82e3-e06e8307c9df"],

Cell[BoxData[
 RowBox[{
  SuperscriptBox["\[Omega]", "2"], " ", 
  RowBox[{"Cos", "[", "\[Theta]", "]"}]}]], "Output",
 CellChangeTimes->{
  3.8406823416644735`*^9, {3.840682379261511*^9, 3.8406823894754925`*^9}, {
   3.840682465476153*^9, 3.8406824751781683`*^9}, {3.8406825416851673`*^9, 
   3.840682567301887*^9}, {3.8406832011680574`*^9, 3.840683277707505*^9}, 
   3.8406833569667234`*^9, 3.840683405470008*^9},
 CellLabel->
  "Out[5383]=",ExpressionUUID->"9cfea2cf-2f77-496f-b2a1-7c1abca853aa"],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{"0", ",", "0", ",", 
   RowBox[{"-", 
    FractionBox[
     RowBox[{"g", " ", "r"}], 
     RowBox[{"Abs", "[", "r", "]"}]]}]}], "}"}]], "Output",
 CellChangeTimes->{
  3.8406823416644735`*^9, {3.840682379261511*^9, 3.8406823894754925`*^9}, {
   3.840682465476153*^9, 3.8406824751781683`*^9}, {3.8406825416851673`*^9, 
   3.840682567301887*^9}, {3.8406832011680574`*^9, 3.840683277707505*^9}, 
   3.8406833569667234`*^9, 3.8406834054750423`*^9},
 CellLabel->
  "Out[5385]=",ExpressionUUID->"b020f211-58c6-4971-9c2a-589ba43bbbe2"]
}, Open  ]]
},
WindowSize->{1520, 781},
WindowMargins->{{-8, Automatic}, {Automatic, 0}},
Magnification:>1.3 Inherited,
FrontEndVersion->"11.3 for Microsoft Windows (64-bit) (2018\:5e743\:670828\
\:65e5)",
StyleDefinitions->"Default.nb"
]
(* End of Notebook Content *)

(* Internal cache information *)
(*CellTagsOutline
CellTagsIndex->{}
*)
(*CellTagsIndex
CellTagsIndex->{}
*)
(*NotebookFileOutline
Notebook[{
Cell[CellGroupData[{
Cell[580, 22, 23537, 492, 2313, "Input",ExpressionUUID->"1874d45f-36c8-481d-a96c-727d8c067141"],
Cell[CellGroupData[{
Cell[24142, 518, 2665, 64, 66, "Print",ExpressionUUID->"7ecd8500-03a8-40bd-822f-895453990cd9"],
Cell[26810, 584, 2786, 69, 94, "Print",ExpressionUUID->"9b424bb9-0d57-4114-bd37-3c837216830e"],
Cell[29599, 655, 1447, 37, 72, "Print",ExpressionUUID->"f3e36976-75d4-4a46-b3ce-dd4c20474e28"],
Cell[31049, 694, 1483, 38, 96, "Print",ExpressionUUID->"0aef69e6-f01e-48af-82a1-f68dbfca13bb"],
Cell[32535, 734, 749, 18, 39, "Print",ExpressionUUID->"c0bcd2c6-29ae-44ec-9683-6cd87e7c7ccc"],
Cell[33287, 754, 1226, 31, 66, "Print",ExpressionUUID->"306517af-c0ec-467f-8122-2e5eaf549686"],
Cell[34516, 787, 1500, 37, 69, "Print",ExpressionUUID->"a739d458-08c7-46fe-b233-96720ac7e606"],
Cell[36019, 826, 1431, 36, 69, "Print",ExpressionUUID->"ecd7aee2-f71d-424e-a11b-2256dbac52c8"],
Cell[37453, 864, 8165, 216, 215, "Print",ExpressionUUID->"a59aaab7-2291-489a-aa3b-eb225bffca07"]
}, Open  ]],
Cell[45633, 1083, 409, 7, 43, "Output",ExpressionUUID->"fdd62302-3f66-4f67-b93e-e37807033b6c"],
Cell[46045, 1092, 477, 9, 43, "Output",ExpressionUUID->"3a7a9d05-1f44-42a0-8952-928e3b75d339"],
Cell[46525, 1103, 474, 9, 43, "Output",ExpressionUUID->"b8fa54e7-534e-40d8-bcd2-bfe3a0f64ac4"],
Cell[47002, 1114, 411, 7, 43, "Output",ExpressionUUID->"3e7ffcc0-9438-4e2d-b432-2c178b37c05f"],
Cell[47416, 1123, 518, 11, 43, "Output",ExpressionUUID->"57b40b92-01df-4de0-82e3-e06e8307c9df"],
Cell[47937, 1136, 499, 10, 43, "Output",ExpressionUUID->"9cfea2cf-2f77-496f-b2a1-7c1abca853aa"],
Cell[48439, 1148, 567, 13, 69, "Output",ExpressionUUID->"b020f211-58c6-4971-9c2a-589ba43bbbe2"]
}, Open  ]]
}
]
*)

